Blue phase (BP) liquid crystals are materials with unique self-assembling properties. They can be regarded as 3D photonic crystals as they organize in 3D cubic structures with sub-micrometer range periodicity and display selective optical bandgaps. Yet, the obtained BP crystals are usually polycrystalline or micrometer-sized monocrystals. Producing large BP monocrystals has proven to be a challenging and time-consuming endeavor, due to BP crystal growth being notoriously slow and the complex requirements for achieving a reasonable size and monocrystalline structure. In this work we successfully obtained large BP monocrystals (single lattice orientation) by fast self-assembly. Our fabrication process, which is about 100× faster than in previous reported research, uses relatively simple techniques, therefore demonstrating a considerable improvement towards the manufacturing of 3D photonic crystals.